Unload templates; disable parent Template Parts using only “theme.json”

Does anyone have any suggestions on how to disable certain template parts in a child theme using theme.json in WordPress with Gutenberg?

Using only theme.json this is not possible, and runs counter to the vision for full site editing.

In the future it’s possible that not only the parent theme templates might be visible, but the templates of previous themes that the user has modified and saved. This has been talked about a lot by the designers working on the site editor, though we haven’t seen it implemented yet. This does mean that at the time of writing it’s extremely unlikely that it can be done entirely using theme.json, and that they might even consider it a bug to be fixed if a way was discovered.

That’s not to say this can’t be done with PHP filters though, but it can’t be done with just theme.json.